So, I went to see an immigration lawyer, told him my story and asked him what to do. He said “Well, you don’t have a funny accent, so just don’t tell anybody that you’re not American and make sure there are no errors on your income tax returns”. I took his advice and worked in the U.S. for the next ten years. I still have my card. I live in Canada now, but it’s great for scooting back and forth across the border. People just smile and wave me through.

And I'm not going to say what the number is because I could end up in a lot
of trouble.

The SSN was created so the Social Security Administration could pay out Social Security benefits. That was its sole original intent. The federal government in 1936 assured the public SSNs would be used only by the SSA. Nowadays, if you are a US person you are required to report any income you receive to the IRS using a SSN. Since anyone who pays you monetary compensation is also required to disclose this income to the IRS, they need your SSN too. You could refuse to give your SSN to the IRS if you wish, the law mandating your disclosure is unclear. This would be rather quixotic and you could end up being subjected to IRS audits for the rest of your life. On the other hand, you might just become a defendant in a case before the Supreme Court and have first-year law students memorize your name forevermore.

There are no laws governing the use of your SSN by private organizations, the government assumes you are old enough to wipe your own ass. If you are asked for your SSN by a company you are doing business with, you are under no compulsion to disclose it. Private organizations use SSNs in different ways and various people may have access to the records, you should not assume the telephone company will guard your SSN as well as you might. Since your SSN has become a passphrase for credit in your name, you should think twice before you provide it to any old McCorp. If you are well informed, persistent and polite, the company you are dealing with will likely back down at some point and agree to use an alternative means of identification or authentication.